Supplementary Variable Approach Applied
to the Transient Analysis of Age-MRSPNs

Miklós Telek, András Horváth

Abstract:

In order to assist the performance evaluation of
complex stochastic models
automatic program tools are developed since a long time.
An effective model description language alternative, supported by
several software tools, is the stochastic Petri net (SPN).
But the attention to the
analytical description and the numerical analysis of non-Markovian
stochastic Petri net models arose only recently.
There are different theoretical approaches and numerical methods
considered in recent works, such as the Markov renewal theory
and the supplementary variable approach, but to find the most
effective way of the analysis of such models
is still a hot research topic.

The supplementary variable approach was succesfully applied
for the transient and steady state analysis of Markov Regerenative
Stochastic Petri Nets (MSRPN) when the
preemption policy associated with the Petri net (PN) transitions
was preemptive repeat different (prd), but it
was not applicable with other preemption mechamisms.
In this paper we extend the
applicability of the supplementary variable approach to
a class of MRSPNs in which
preemptive resume (prs)
policy can also be assigned to the PN transitions.